A cylindrical pencil of 2 cm diameter is sharpened so as to produce a perfect hemispherical portion

M4maths Previous Puzzles

06 Nov 2015 Volume

A cylindrical pencil of 2 cm diameter is sharpened so as to produce a perfect hemispherical portion at one end and a perfect conical portion of length 2 cm at the other end. Find the volume of shavings.

OPtion

1) 6.364 cm^3
2) 6.354 cm^3
3) 5.953 cm^3
4) 5.979 cm^3
5) 5.834 cm^3
6) 6.543 cm^3
7) 5.923 cm^3
8) 6.246 cm^3
9) 5.238 cm^3
10)None of these

Solution

For each portion
Volume of shavings = Volume of original cylindrical portion - Volume of final portion (Conical and Hemispherical)
and r = 1 cm
Volume of hemispherical portion = 2/3 Pi 1^3 = 2*Pi/3
Volume of conical portion = 1/3*Pi*1^2*2 = 2*Pi / 3
Total volume of cylindrical portion of both ends =
Pi(1)^2*1 + Pi(1)^2*2 = 3 Pi
Volume of shavings = Total volume of cylindrical portion - Volume of conical portion - Volume of hemispherical portion
3 Pi - 2Pi/2 - 2Pi/3 = 3Pi - 4Pi/3 = 5Pi/3
Using Pi = 22/7
5*22 / 21
5.238 cm^3
Option 9)

Correct Option: 9 Best Solution (2)

Jaikumar Bhatia   9 years AGO

Dia. of Cylinder/cone/hemispher=d=2cm
Radii of Cylinder/cone/hemisphere=r=d/2=1cm..........(i)
(l) cone=h1=2cm......................................................................(ii)
(l)cylinder=(l)cone+radii of hemisphere
h=h1+r
=2+1
=3cm................................................................(iii)
V(shavings)=V(cyl)-V(cone)-V(hemisphere)
=(pi*r^2*h)-(1/3*pi*r^2*h1)-(2/3*pi*r^3)
=5.238cm^3.............................(from i,ii,iii)
Option :(9)

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PRABHAT KUMAR   9 years AGO

Volume of cylinder pi*1*3=3*pi
Vol of hemisphere & Vol of cone=2/3*pi*1+1/3*pi*2=4/3*pi
Vol of savings =3*pi-4/3*pi=5/3*pi=5.238cm^3

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